Understanding interacting aerofoils with complex analysis

Abstract: When two or more aerofoils move together, their interactions can significantly affect the characteristics of the surrounding fluid. We develop a rigorous mathematical theory for these interactions using conformal maps, multiply connected function theory, and modified Schwarz problems. Via the transcendental Schottky–Klein prime function, our theory is valid for any connectivity (any number of aerofoils). Accordingly, our approach is very general and permits many aerofoil motions (pitching, heaving, undulatory) and configurations (tandem, in-line, ground effect). We focus on the (doubly connected) case where there are two interacting swimmers and find that our theory yields excellent agreement with experimental data. We also develop an asymptotic solution that captures the salient features of the prime function solution.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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